The present invention is directed to an optical fiber having a multiple-clad core, and in particular to an improved W-fiber having a threshold cladding layer in order to provide low dispersion at a wide range of wavelengths.
Optical signals in single-mode fibers suffer distortion due to the fact that the fundamental mode delay t.sub.g changes with wavelength .lambda.. For a step-index fiber having a core surrounded by a single layer of cladding material, FIG. 1A shows how the effective group-index of the fundamental mode N'=ct.sub.g /L depends qualitatively on wavelength. (See L. G. Cohen and W. L. Mammel: Low-loss quadruple-clad single-mode-light guides with dispersion below 2 ps/km nm over the 1.28 .mu.m -1.65 .mu.m wavelength range, Electron. Lett. 18 (1982) 1023-1024). Here c is the vacuum velocity of light and L is the length of the fiber. The dotted curves designated by n.sub.co ' and n.sub.cl ' represent the group-indices of the core and the cladding material, respectively. The group-index n' of a material is related to the index of refraction n of the material by the relationship: ##EQU1##
At short wavelengths (corresponding to the values of the fiber parameter V =(2.pi.a/.lambda.).sqroot.n.sub.co.sup.2 -n.sub.cl.sup.2 larger than 3, with a as the core radius), the fundamental mode fields are well concentrated within the core so that this mode propagates at a rate that depends substantially upon the group-index of the core material. With increasing wavelength the fields extend ever wider into the cladding so that eventually the fundamental mode propagates at a rate depending substantially upon the group-index of the cladding. This is shown in FIG. lA, which illustrates that the effective group-index N' of a fiber having a core surrounded by a layer of cladding material is close to the group-index n.sub.co ' of the core at short wavelengths and approaches the group-index n.sub.cl ' at long wavelengths.
The group-index of fused silica has a minimum near .lambda.=1.28 .mu.m. Doping fused silica with germanium or phosphor to raise its refractive index in the fiber core or with fluorine to lower its refractive index in the cladding shifts this minimum only slightly. The effective group-index of a fiber having a core surrounded by a layer of cladding material will also pass through a minimum, as illustrated by the dip in N' in FIG. lA, as the fundamental mode makes its transition from the core group-index to the cladding group-index with increasing wavelength. To the first order, at such a minimum in the effective group-index of a fiber the fundamental mode delay becomes independent of wavelength and the dispersion D of the fiber becomes minimal. At such a minimum the slope of the delay characteristic vanishes and only its curvature (that is, higher derivative components) remains to distort signals, yet by orders of magnitude less. However, for such a dispersion minimum to be of any use for signal transmission it must be at a long enough wavelength so that the core guides only the fundamental mode, yet not too long a wavelength, lest the fundamental mode fields extend too far out into the cladding and become too sensitive to fiber bending. The dispersion must for these two reasons occur in the wavelength range where the effective group-index of the fundamental mode transits from the group-index of the core to that of the cladding. Simple step-index fibers as well as gradient-index fibers without any index depression below the cladding index can be designed to have one dispersion minimum in the useful single-mode range, but only at wavelengths somewhat longer than that of the material dispersion minimum at.lambda..perspectiveto.1.28 .mu.m (see K. Jurgensen: Dispersion minimum of monomode fibers, Appl. Opt. 18 (1979 ) 1259-1261; L. Jeunhomme: dispersion minimization in single-mode fibers between 1.3 .mu.m and 1.7 m, Electron. Lett. 15 (1979) 478-479; H. Tsuchiya and N. Imoto: Dispersion-free single-mode fiber in 1.5 .mu.m wavelength region, Electron. Lett. 15 (1979) 476-478; L. G. Cohen et al: Tailoring zero chromatic dispersion into the 1.5-1.6 .mu.m low loss spectral region of single-mode fibers, Electron. Lett. 15 (1979) 334-335; and B. J. Ainslie et al: Monomode fiber with ultra-low loss and minimum dispersion at 1.55 .mu.m, Electron. Lett. 18 (1982) 842-844).
It is known that an additional layer of cladding material can be added, and that the resulting fiber exhibits a modified effective group-index. This can result in a fiber having a W-index profile with an annular cross-sectional region of depressed index surrounding the core (that is, along a line through the center of the fiber the index of refraction dips between the outer cladding and the core and dips again between the core and the outer cladding, so that the index of refraction varies in the manner of a stylized W along the diameter of the fiber), the effective group-index of the fundamental mode in making its transition with increasing wavelength from the group-index of the core to that of the cladding will be affected by the lower index n.sub.w of the intermediate layer and tend to approach its group-index n.sub.w '. In a suitably designed W-fiber (see K. Okamoto et al: Dispersion minimization in single-mode fibers over a wide spectral range, Electron. Lett. 15 (1980) 729-731; T. Miya et al: Fabrication of low dispersion single-mode fibers over a wide spectral range, IEEE J. QE 17 (1981) 858-861; and L. G. cohen et al: Tailoring the shapes of dispersion spectra to control band widths in single-mode fibers, Opt. Lett. 7 (1982) 183-185) the effective group-index of the fundamental mode will, with increasing wavelength, first pass a minimum and, after increasing somewhat, pass a maximum and turn down again, as it is o shown in FIG. lA by the line designated with N.sub.w '. When N.sub.w ' approaches n.sub.cl ', or even crosses it, the fundamental mode fields will extend far out into the cladding and become very sensitive to fiber bending, or the fundamental mode will even be cut off. Such a W-fiber cannot be operated at wavelengths much beyond the maximum of N.sub.w '.
The fundamental mode of the optical fiber is that particular guided mode of propagation which, with increasing values of the fiber parameter V=(2.pi.a/.lambda.).sqroot.n.sub.co.sup.2 -n.sub.cl.sup.2, is the first one to be guided by the fiber core, and, for a certain range of values of the fiber parameter V up to the cutoff value of the next higher order modes, also the only mode which the fiber core guides. a is the radius of the fiber core. The group index n' of a material is defined by relations (1). The effective group index N' of a mode of propagation of an optical waveguide is defined by the relationship ##EQU2## where N is the effective index of this mode of propagation and related to its phase coefficient .beta. and the wavenumber k=2.pi./.lambda.by the relationship EQU N=.beta./k